CURE: Interdisciplinary Undergraduate Research: Enumerating Self-Avoiding Walks

Enumerating Self-Avoiding Walks

CURE: Interdisciplinary Undergraduate Research: Enumerating Self-Avoiding Walks

Presenter

Christopher Krause

Mentor

Dr. Anne Donnelly

College

Herbert Wertheim College of Engineering

Abstract

A self-avoiding walk is a series of moves on the lattice grid that does not revisit the same point twice. Although these mathematical structures are simple to define and understand, they exhibit extremely complex and unpredictable behavior. In my project, I attempt to calculate the number of “block self-avoiding walks” of length n on the lattice grid. Simple solutions to this problem have repeatedly eluded the cleverest of problem-solvers. Currently, only 35 terms of the sequence have been found. Here, I present a novel approach to the classic combinatorics problem that can be applied to other types of self-avoiding walks.

Poster

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Research Pitch

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